Pi me a River

Is the average sinuosity of the world's rivers equal to π?

What is this?

There is a hypothesis that the average sinuosity of the
world's rivers should be equal to π (3.141593). Numberphile produced a
video discussing the idea
and stated that there didn't seem to be any recorded data to actually check to see if it is true. This
project aims to solve that.

Sinuosity is the ratio of the river's length to the straight-line distance between its source and mouth.
For example, the Amazon is 6992.0km long and has a direct straight-line distance of 3026.7km, giving it a
sinuosity of 6992.0 / 3026.7 = 2.31, notably less than π.

Notes on accuracy

This data has been crowd sourced and so is potentially guesswork and estimations. It is often difficult to
find the exact source of a river, and indeed many rivers have multiple sources that are debated. Furthermore
some named rivers are tributaries to larger rivers and different lengths are given depending on how you look
at the data.

Results

With 280 rivers the average
sinuosity is 1.916233,
with a standard deviation of 0.730769.

This is a difference of 1.22536 from π,
or an error of 39.004415%.

Distribution

Length vs Sinuosity

Code

The code for this project is available at github.
If you are interested in getting involved, either just submit your local river to the right or contribute
and discuss via github.

Todo

I intend to continue updating the site with some interface improvements and potentially importing a massive
set of data on rivers to improve the accuracy of the results.

Add your river

pimeariver.com is undergoing a major rebuild which will involve
importing the river data for the entire globe from Open Street Map.

In the meantime adding your own rivers has been disabled to
prevent the data from being spammed. Sorry for any inconvenience,
you can follow the
updates progress on github.